The "legend" is that every civilization gets buried under a thick layer of earth, so we'd have to dig real deep, hundreds of kilometers deep, to find anything.

Our nuclear age predated the moon landing, though that doesn't seem to be necessary (this is relevant because radiocarbon dating is impacted by nukes; we should see records of that if it happened).

The moon isn't a static place, though. Meteors slowly change its face, and artifacts may well be buried there. Putting big and durable monuments on the moon would be quite the expensive endeavor, so we'd have to do some significant lunar archaeology to really rule it out.

Ocean floor isn't static, either; stuff gets swallowed by subduction zones on geological timescales. Not to mention falling debris and ocean life tend to build up; I wouldn't expect artifacts from 1Mya to be sitting out in the open.

I like the idea of putting artifacts on the moon, just for this purpose. And also on any comet or asteroid that happens to wander by. The reasoning is this: The golden rule. Perhaps we can answer the question, for some other future intelligent civilization, long after we are gone. At least someone can know, they were not alone.

A space probe like Voyager might be our best bet. It's easier to detect an object traveling through space than one on a planet. Something on the moon will eventually become buried due to impacts.

Is the life expectancy of Voyager in deep space really higher than when it would be placed on the moon?

I wouldn’t know. On the plus side, in space it doesn’t have the moon’s gravity pulling stuff towards it, and doesn’t run the risk of matter already on the moon being thrown towards it from near direct hits.

On the minus side, in space it isn’t shielded from direct impacts from at least half of all directions (≈ half by the moon, a bit more by earth, if placed on the earth-facing side of the moon)

IIRC the Voyager probes aren't on the eliptic plane, they're less likely to hit debris. Plus once they reach the interstellar medium there is not much to worry about besides cosmic rays.